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## Homework Statement

2. The Celsius temperature in a region of space is given by T(x, y, z) = 2x^2 − xyz. A

particle is moving in this region with its position at time t given by x = 2t^2, y = 3t,

z = −t^2, where time and distance are measured in seconds and meters, respectively.

(a) Find the rate of change of the temperature experienced by the particle in C◦/m

when the particle is at the point P(8, 6,−4).

(b) Find the rate of change of the temperature experienced by the particle in C◦/sec

at P.

## Homework Equations

## The Attempt at a Solution

To find part a, we need to find the direction vector. However, how to find direction vector? Is velocity vector the direction vector?

If so, than part b is very easy.

Since [itex]\frac{dT}{dt}[/itex]=[itex]\frac{dT}{ds}\frac{ds}{dt}[/itex]

Where [/itex]=[itex]\frac{ds}{dt}[/itex] is the magnitute of velocity.

I wonder whether I am correct.